Question

verify whether x cube minus 3 x square - 10 X + 24 is divisible by X square + X - 6 or not how can you verify using factor theorem​

Answer 1

Answer:

Verify using factor theorem, whether 2x

4

−6x

3

+3x

2

+3x−2 is divisible by x

2

−3x+2 or not?

Medium

Solution

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The divisor is not a linear polynomial, it is a quadratic polynomial.

Let us factorize the divisor :

x

2

−3x+2

= x

2

−2x−x+2

= x(x−2)−1(x−2)

= (x−1)(x−2)

Then (x−1) and (x−2) are factors of polynomial x

2

−3x+2.

Let p(x)=2x

4

−6x

3

+3x

2

+3x−2

If (x−1) and (x−2) both are factors of p(x), then for x=1 and x=2, p(x) should be 0.

On replacing x by 1, we get

p(1)=2(1)

4

−6(1)

3

+3(1)

2

+3(1)−2

⇒p(1)=2−6+3+3−2=0

On replacing x by 2, we get

p(2)=2(2)

4

−6(2)

3

+3(2)

2

+3(2)−2

⇒p(2)=32−48+12+6−2=0

So, (x−1) and (x−2) are factors of p(x),

Hence, p(x)=2x

4

−6x

3

+3x

2

+3x−2 is divisible by x

2

−3x+2.

Step-by-step explanation:

your answer is above .